Finite Group Databasebeta

← #34116141

Subgroups — #34116141

Order 20096.

360 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758340C211yesmaximal, characteristic
2#23758266C212yesmaximal, complemented
3D157⋊#100C211yesmaximal, characteristic
4#23758144C212yesmaximal, complemented
5#124×D157C211yesmaximal, characteristic
6D157⋊M16C2212yes—
7D4×#10597845—24no—
8#19097850C2212yes—
9C2×C22⋊#10597845—22no—
10#19097834—24no—
11#19097831—22no—
12C2×Q8×D157C2211yescharacteristic
13C2×D4×D157C2211yescharacteristic
14#19097760C411yescharacteristic, complemented
15#19097759C411yescharacteristic, complemented
16#19097758C411yescharacteristic, complemented
17#19097757—22no—
18C22⋊C4×D157—22no—
19C42×D157C2211yescharacteristic
20#124×C157C411yescharacteristic, complemented
21C22×#10597845—24no—
22#14578964—22no—
23#14578963—22no—
24D157⋊C8—22no—
25C4⋊#10597845D414yes—
26C22⋊#10597845—24no—
27C22⋊#10597845—22no—
28C4×#10597845—22no—
29C23×D157D412yes—
30C2×Dic314—21no—
31C2×Dic314C2×C411yescharacteristic, complemented
32Q8×D157—22no—
33Q8×D157—22no—
34C2×D628C2×C411yescharacteristic
35C2×C22⋊D157D412yes—
36D4×D157—22no—
37D4×D157—22no—
38C2×C4×D157—21no—
39C2×C4×D157—21no—
40C2×C4×D157C2311yescharacteristic
41C22⋊Dic157—22no—
42#14578931—22no—
43#14578931—22no—
44C4×Dic157—21no—
45C4×Dic157C2×C411yescharacteristic, complemented
46C2×Q8×C157C2×C411yescharacteristic, complemented
47C2×D4×C157C2×C411yescharacteristic
48C22⋊C4×C157—22no—
49C42×C157C2×C411yescharacteristic, complemented
50C2×#10597845—24no—
51C2×#10597845—84no—
52#11929441—42no—
53C22×D157—22no—
54C22×D157—22no—
55C22×D157—44no—
56C22×D157C22⋊C412yes—
57C22×D157C2×D411yescharacteristic
58Dic314—22no—
59Dic314—42no—
60D628—22no—
61C22⋊D157—24no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157C2×D411yescharacteristic
65C4×D157—42no—
66C4×D157—41no—
67C4×D157—41no—
68C4×D157C2×D412yes—
69C4×D157#4112yes—
70C23×C157C22⋊C412yes—
71Q8×C157—22no—
72D4×C157—22no—
73C2×C4×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157C22×C411yescharacteristic
76C22×C157—22no—
77C22×C157—42no—
78C22×C157C2×C22⋊C411yescharacteristic
79C2×D157—22no—
80C2×D157—22no—
81C2×D157—44no—
82C2×D157—42no—
83C2×D157—82no—
84C2×D157#12011yescharacteristic
85C2×D157#12311yescharacteristic
86#10597845—44no—
87C4×C157—41no—
88C4×C157—41no—
89C4×C157C4×D412yes—
90Dic157—41no—
91Dic157—41no—
92Dic157#12112yes—
93C2×C157—21no—
94C2×C157—42no—
95C2×C157#38611yescharacteristic
96D157—21no—
97D157—42no—
98D157#45512yes—
99C157#188511yescharacteristic, complemented, Sylow
100#1885—1571nomaximal, Sylow
101C2×#124—1571no—
102#518—1571no—
103#419—1572no—
104C2×#100—1571no—
105#339—1572no—
106C22×Q8—1571no—
107C22×D4—1571no—
108C2×M16—1572no—
109#124—3142no—
110#124—1571no—
111#124—1571no—
112#124—1571no—
113#124#1059784511yescharacteristic, complemented
114C4×D4—3144no—
115#117—1572no—
116C2×C22⋊C4—3142no—
117C2×C22⋊C4—3142no—
118C2×C42—1571no—
119#103—3144no—
120#100—3142no—
121C24—1572no—
122C2×Q8—3141no—
123C2×Q8—3142no—
124C2×Q8—3142no—
125C2×Q8—1571no—
126C2×Q8C2×#1059784511yescharacteristic, complemented
127C2×D4—3142no—
128C2×D4—3142no—
129C2×D4—1572no—
130C2×D4—1571no—
131C2×D4C2×#1059784511yescharacteristic
132C22×C4—3141no—
133C22×C4—3141no—
134C22×C4—3144no—
135C22×C4—1571no—
136M16—3142no—
137M16—3142no—
138C2×C8—3142no—
139C4⋊C4—1574no—
140C22⋊C4—22no—
141C22⋊C4—3142no—
142C22⋊C4—3142no—
143C22⋊C4—3144no—
144C22⋊C4—3142no—
145C22⋊C4—3142no—
146C42—3141no—
147C42—3142no—
148C42—1571no—
149C42C2×#1059784511yescharacteristic, complemented
150C23—3142no—
151C23—3142no—
152C23—6284no—
153C23—1571no—
154C23—1572no—
155C23C22⋊#1059784512yes—
156Q8—22no—
157Q8—3142no—
158Q8—6282no—
159D4—22no—
160D4—3144no—
161D4—3142no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—3144no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—6282no—
168C2×C4—6281no—
169C2×C4—6281no—
170C2×C4—1571no—
171C2×C4—1572no—
172C2×C4—1572no—
173C2×C4—12564no—
174C2×C4C22×#1059784511yescharacteristic
175C8—6282no—
176C22—22no—
177C22—42no—
178C22—3142no—
179C22—3142no—
180C22—6282no—
181C22—6284no—
182C22—1571no—
183C22—1571no—
184C22—12562no—
185C22C2×C22⋊#1059784511yescharacteristic
186C4—41no—
187C4—41no—
188C4—6281no—
189C4—6284no—
190C4—6281no—
191C4—1572no—
192C4D4×#1059784512yes—
193C2—21no—
194C2—42no—
195C2—3141no—
196C2—6282no—
197C2—1572no—
198C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#124×C157C4
socleC2×C157#386
prime radicalC2×D4×D157C22
cosocleC2×C4×D157C23
hypercenter#124#10597845
hypocenterC157#1885
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23758266C2semidirect
4. #23758144C2semidirect
14. #19097760C4semidirect
15. #19097759C4semidirect
16. #19097758C4semidirect
20. #124×C157C4semidirect
31. C2×Dic314C2×C4semidirect
45. C4×Dic157C2×C4semidirect
46. C2×Q8×C157C2×C4semidirect
49. C42×C157C2×C4semidirect
99. C157#1885semidirect
113. #124#10597845semidirect
126. C2×Q8C2×#10597845semidirect
149. C42C2×#10597845semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237583402
#237582662
D157⋊#1002
#237581442
#124×D1572
#1885157